Question: $J$ is the midpoint of $\overline{CT}$ $C$ $J$ $T$ If: $ CJ = 7x - 5$ and $ JT = 9x - 13$ Find $CT$.
Solution: A midpoint divides a segment into two segments with equal lengths. ${CJ} = {JT}$ Substitute in the expressions that were given for each length: $ {7x - 5} = {9x - 13}$ Solve for $x$ $ -2x = -8$ $ x = 4$ Substitute $4$ for $x$ in the expressions that were given for $CJ$ and $JT$ $ CJ = 7({4}) - 5$ $ JT = 9({4}) - 13$ $ CJ = 28 - 5$ $ JT = 36 - 13$ $ CJ = 23$ $ JT = 23$ To find the length $CT$ , add the lengths ${CJ}$ and ${JT}$ $ CT = {CJ} + {JT}$ $ CT = {23} + {23}$ $ CT = 46$